There are several types of head bobs. Some indicate a
passive or submissive presence, while others are a sign of
dominance. The first of the two videos to the right, show
male Beardies displaying their territorial and mating head
bob. During the filming, there were videos of females
displaying passive gestures, which is what excited them
enough to display dominance. The head bob more often
displayed by males is rapid and agressive. Sometimes the
motion shakes their whole body. As you will see, a display
of their blackened beards often accompanies the aggressive
head bob.

The female footage shows a slower, more passive form of head
bob. This footage was taken when the females were younger,
and influenced by the presence of males across the room. The
female head bob is often accompanied with the
arm wave behavior, as is
shown.

Bearded dragons will use these gestures to communicate to
each other in a social context. The chosen behavior will
indicate the intention of the animal. Often with two males,
there will be a conflict, and head bobs will turn into a
fight. The winner gains dominance of the territory. Yes,
bearded dragons can be territorial, especially the males.

These social behaviors are used to define a semi-hierarchy.
Males typically dominate a given territory, but females will
also have a ranking in seniority. From what I've seen,
females aren't typically agressive to show dominance.
Usually size will dictate seniority, and the smaller females
show signs of submission before a confrontation is
necessary.

An important thing to keep in mind, is that the behaviors
shown are not necessarily specific to either sex. Many
people try to judge the sex of their dragon based on their
behavior. Females can and do display the agressive type head
bobbing, but it is less common. And males will display the
more submissive head bobbing. This is actually more common
than you might think. Especially when a male beardie is
young, they will display the submissive behavior. This makes
sense, as they are quite small, and don't really have much
to back agressive territorial claims. For more information
on sexing your beardie, check out the
Sexing Your Bearded Dragon
article.